Question

what is the volume of this figure? 2 in. 2 in. 3 in. 4 in. 3 in. 1 in. 5 in. 2 in. cubic inches submit

Explanation:

Step1: Split the figure into two rectangles

We can split the L - shaped figure into two rectangular prisms. The first one has dimensions \(2\) in (length) \(\times2\) in (width) \(\times4\) in (height). The second one has dimensions \(3\) in (length) \(\times2\) in (width) \(\times1\) in (height).

Step2: Calculate the volume of the first prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the first prism, \(l = 2\), \(w = 2\), \(h = 4\). So \(V_1=2\times2\times4 = 16\) cubic inches.

Step3: Calculate the volume of the second prism

For the second prism, \(l = 3\), \(w = 2\), \(h = 1\). Using the volume formula \(V = l\times w\times h\), we get \(V_2=3\times2\times1=6\) cubic inches.

Step4: Sum the volumes of the two prisms

To find the total volume of the figure, we add the volumes of the two prisms together. So \(V = V_1+V_2=16 + 6=22\) cubic inches.

Answer:

22